{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Implementing a simple perceptron in python - theano version"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pylab as pl\n",
    "import numpy as np\n",
    "import matplotlib.cm as cm\n",
    "import sklearn.cross_validation as skcross\n",
    "%matplotlib inline\n",
    "\n",
    "np.set_printoptions(precision=5, suppress=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Very quick introduction to theano\n",
    "\n",
    "[Theano](http://www.deeplearning.net/software/theano/) is basically a code generator that compiles mathematical expressions into computer code.\n",
    "\n",
    "The basic idea to keep in mind is that when using Theano, you work with *symbolic* variables, like you do when you write mathematical expressions. It is only when you call *theano.function* that code\n",
    "(GPU code if you target the GPU, numpy code if you target the CPU) gets generated to compute your function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Note that this require a kernel restart to be effective\n",
    "import os\n",
    "os.environ['THEANO_FLAGS'] = 'device=cpu'\n",
    "#os.environ['THEANO_FLAGS'] = 'device=gpu'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "device :  cpu\n"
     ]
    }
   ],
   "source": [
    "import theano.tensor as T\n",
    "import theano\n",
    "import tempfile\n",
    "import pydot\n",
    "from IPython.display import SVG\n",
    "from IPython.display import display\n",
    "\n",
    "print 'device : ', theano.config.device"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def show_computation_graph(fn):\n",
    "    \"\"\"\n",
    "    Wrapper around theano.printing.pydotprint that show the computation graph\n",
    "    for a given theano function\n",
    "    Args:\n",
    "        fn: the function for which to show the computation graph\n",
    "        \n",
    "    This requires pydot and graphviz\n",
    "    \"\"\"\n",
    "    display(SVG(theano.printing.pydotprint(fn, return_image=True, format='svg')))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We will start with simple theano expressions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### a*x + b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "13.0\n"
     ]
    },
    {
     "data": {
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       "<svg height=\"216pt\" viewBox=\"0.00 0.00 709.41 216.00\" width=\"709pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n",
       "<g class=\"graph\" id=\"graph0\" transform=\"scale(1 1) rotate(0) translate(4 212)\">\n",
       "<title>G</title>\n",
       "<polygon fill=\"white\" points=\"-4,4 -4,-212 705.407,-212 705.407,4 -4,4\" stroke=\"none\"/>\n",
       "<!-- Elemwise{Composite{((i0 * i1) + i2)}} -->\n",
       "<g class=\"node\" id=\"node1\"><title>Elemwise{Composite{((i0 * i1) + i2)}}</title>\n",
       "<ellipse cx=\"344.611\" cy=\"-104\" fill=\"#ffaabb\" rx=\"150.901\" ry=\"18\" stroke=\"black\"/>\n",
       "<text font-family=\"Times,serif\" font-size=\"14.00\" text-anchor=\"middle\" x=\"344.611\" y=\"-99.8\">Elemwise{Composite{((i0 * i1) + i2)}}</text>\n",
       "</g>\n",
       "<!-- TensorType(float32, scalar) -->\n",
       "<g class=\"node\" id=\"node5\"><title>TensorType(float32, scalar)</title>\n",
       "<polygon fill=\"blue\" points=\"429.154,-36 260.069,-36 260.069,-0 429.154,-0 429.154,-36\" stroke=\"black\"/>\n",
       "<text font-family=\"Times,serif\" font-size=\"14.00\" text-anchor=\"middle\" x=\"344.611\" y=\"-13.8\">TensorType(float32, scalar)</text>\n",
       "</g>\n",
       "<!-- Elemwise{Composite{((i0 * i1) + i2)}}&#45;&gt;TensorType(float32, scalar) -->\n",
       "<g class=\"edge\" id=\"edge4\"><title>Elemwise{Composite{((i0 * i1) + i2)}}-&gt;TensorType(float32, scalar)</title>\n",
       "<path d=\"M344.611,-85.5951C344.611,-74.2572 344.611,-59.2271 344.611,-46.3153\" fill=\"none\" stroke=\"black\"/>\n",
       "<polygon fill=\"black\" points=\"348.111,-46.0951 344.611,-36.0952 341.111,-46.0952 348.111,-46.0951\" stroke=\"black\"/>\n",
       "<text font-family=\"Times,serif\" font-size=\"14.00\" text-anchor=\"middle\" x=\"421.382\" y=\"-56.8\">TensorType(float32, scalar)</text>\n",
       "</g>\n",
       "<!-- name=a TensorType(float32, scalar) -->\n",
       "<g class=\"node\" id=\"node2\"><title>name=a TensorType(float32, scalar)</title>\n",
       "<polygon fill=\"green\" points=\"217.334,-208 -0.111442,-208 -0.111442,-172 217.334,-172 217.334,-208\" stroke=\"black\"/>\n",
       "<text font-family=\"Times,serif\" font-size=\"14.00\" text-anchor=\"middle\" x=\"108.611\" y=\"-185.8\">name=a TensorType(float32, scalar)</text>\n",
       "</g>\n",
       "<!-- name=a TensorType(float32, scalar)&#45;&gt;Elemwise{Composite{((i0 * i1) + i2)}} -->\n",
       "<g class=\"edge\" id=\"edge1\"><title>name=a TensorType(float32, scalar)-&gt;Elemwise{Composite{((i0 * i1) + i2)}}</title>\n",
       "<path d=\"M127.843,-171.818C140.816,-161.117 158.798,-147.924 176.815,-140 196.099,-131.52 217.548,-125.053 238.49,-120.135\" fill=\"none\" stroke=\"black\"/>\n",
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       "<text font-family=\"Times,serif\" font-size=\"14.00\" text-anchor=\"middle\" x=\"259.509\" y=\"-142.8\">0 TensorType(float32, scalar)</text>\n",
       "</g>\n",
       "<!-- name=x TensorType(float32, scalar) -->\n",
       "<g class=\"node\" id=\"node3\"><title>name=x TensorType(float32, scalar)</title>\n",
       "<polygon fill=\"green\" points=\"453.62,-208 235.603,-208 235.603,-172 453.62,-172 453.62,-208\" stroke=\"black\"/>\n",
       "<text font-family=\"Times,serif\" font-size=\"14.00\" text-anchor=\"middle\" x=\"344.611\" y=\"-185.8\">name=x TensorType(float32, scalar)</text>\n",
       "</g>\n",
       "<!-- name=x TensorType(float32, scalar)&#45;&gt;Elemwise{Composite{((i0 * i1) + i2)}} -->\n",
       "<g class=\"edge\" id=\"edge2\"><title>name=x TensorType(float32, scalar)-&gt;Elemwise{Composite{((i0 * i1) + i2)}}</title>\n",
       "<path d=\"M344.611,-171.595C344.611,-160.257 344.611,-145.227 344.611,-132.315\" fill=\"none\" stroke=\"black\"/>\n",
       "<polygon fill=\"black\" points=\"348.111,-132.095 344.611,-122.095 341.111,-132.095 348.111,-132.095\" stroke=\"black\"/>\n",
       "<text font-family=\"Times,serif\" font-size=\"14.00\" text-anchor=\"middle\" x=\"426.509\" y=\"-142.8\">1 TensorType(float32, scalar)</text>\n",
       "</g>\n",
       "<!-- name=b TensorType(float32, scalar) -->\n",
       "<g class=\"node\" id=\"node4\"><title>name=b TensorType(float32, scalar)</title>\n",
       "<polygon fill=\"green\" points=\"689.62,-208 471.603,-208 471.603,-172 689.62,-172 689.62,-208\" stroke=\"black\"/>\n",
       "<text font-family=\"Times,serif\" font-size=\"14.00\" text-anchor=\"middle\" x=\"580.611\" y=\"-185.8\">name=b TensorType(float32, scalar)</text>\n",
       "</g>\n",
       "<!-- name=b TensorType(float32, scalar)&#45;&gt;Elemwise{Composite{((i0 * i1) + i2)}} -->\n",
       "<g class=\"edge\" id=\"edge3\"><title>name=b TensorType(float32, scalar)-&gt;Elemwise{Composite{((i0 * i1) + i2)}}</title>\n",
       "<path d=\"M561.446,-171.815C548.516,-161.112 530.589,-147.919 512.611,-140 493.311,-131.499 471.838,-125.023 450.871,-120.102\" fill=\"none\" stroke=\"black\"/>\n",
       "<polygon fill=\"black\" points=\"451.481,-116.652 440.958,-117.879 449.949,-123.482 451.481,-116.652\" stroke=\"black\"/>\n",
       "<text font-family=\"Times,serif\" font-size=\"14.00\" text-anchor=\"middle\" x=\"619.509\" y=\"-142.8\">2 TensorType(float32, scalar)</text>\n",
       "</g>\n",
       "</g>\n",
       "</svg>"
      ],
      "text/plain": [
       "<IPython.core.display.SVG at 0x105e16b10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "a = T.scalar('a', dtype='float32')\n",
    "b = T.scalar('b', dtype='float32')\n",
    "x = T.scalar('x', dtype='float32')\n",
    "\n",
    "res = a*x + b\n",
    "\n",
    "# compile the function for our target device (GPU or CPU)\n",
    "res_f = theano.function(inputs=[a, b, x], outputs=res)\n",
    "\n",
    "print res_f(a=2, b=3, x=5)\n",
    "\n",
    "show_computation_graph(res_f)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### sigmoid(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = T.scalar('x', dtype='float32')\n",
    "sigmoid_x = T.nnet.sigmoid(x)\n",
    "f_x = theano.function(inputs=[x], outputs=sigmoid_x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array(0.7310585975646973, dtype=float32)"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f_x(1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x105ec4d10>]"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x105ef4490>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "xvals = np.linspace(-6, 6, num=50, dtype=np.float32)\n",
    "yvals = [f_x(v) for v in xvals]\n",
    "pl.plot(xvals, yvals)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/svg+xml": [
       "<svg height=\"216pt\" viewBox=\"0.00 0.00 270.55 216.00\" width=\"271pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n",
       "<g class=\"graph\" id=\"graph0\" transform=\"scale(1 1) rotate(0) translate(4 212)\">\n",
       "<title>G</title>\n",
       "<polygon fill=\"white\" points=\"-4,4 -4,-212 266.546,-212 266.546,4 -4,4\" stroke=\"none\"/>\n",
       "<!-- sigmoid -->\n",
       "<g class=\"node\" id=\"node1\"><title>sigmoid</title>\n",
       "<ellipse cx=\"109.004\" cy=\"-104\" fill=\"#ffaabb\" rx=\"38.7128\" ry=\"18\" stroke=\"black\"/>\n",
       "<text font-family=\"Times,serif\" font-size=\"14.00\" text-anchor=\"middle\" x=\"109.004\" y=\"-99.8\">sigmoid</text>\n",
       "</g>\n",
       "<!-- TensorType(float32, scalar) -->\n",
       "<g class=\"node\" id=\"node3\"><title>TensorType(float32, scalar)</title>\n",
       "<polygon fill=\"blue\" points=\"193.547,-36 24.4618,-36 24.4618,-0 193.547,-0 193.547,-36\" stroke=\"black\"/>\n",
       "<text font-family=\"Times,serif\" font-size=\"14.00\" text-anchor=\"middle\" x=\"109.004\" y=\"-13.8\">TensorType(float32, scalar)</text>\n",
       "</g>\n",
       "<!-- sigmoid&#45;&gt;TensorType(float32, scalar) -->\n",
       "<g class=\"edge\" id=\"edge2\"><title>sigmoid-&gt;TensorType(float32, scalar)</title>\n",
       "<path d=\"M109.004,-85.5951C109.004,-74.2572 109.004,-59.2271 109.004,-46.3153\" fill=\"none\" stroke=\"black\"/>\n",
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       "<text font-family=\"Times,serif\" font-size=\"14.00\" text-anchor=\"middle\" x=\"185.775\" y=\"-56.8\">TensorType(float32, scalar)</text>\n",
       "</g>\n",
       "<!-- name=x TensorType(float32, scalar) -->\n",
       "<g class=\"node\" id=\"node2\"><title>name=x TensorType(float32, scalar)</title>\n",
       "<polygon fill=\"green\" points=\"218.013,-208 -0.00439471,-208 -0.00439471,-172 218.013,-172 218.013,-208\" stroke=\"black\"/>\n",
       "<text font-family=\"Times,serif\" font-size=\"14.00\" text-anchor=\"middle\" x=\"109.004\" y=\"-185.8\">name=x TensorType(float32, scalar)</text>\n",
       "</g>\n",
       "<!-- name=x TensorType(float32, scalar)&#45;&gt;sigmoid -->\n",
       "<g class=\"edge\" id=\"edge1\"><title>name=x TensorType(float32, scalar)-&gt;sigmoid</title>\n",
       "<path d=\"M109.004,-171.595C109.004,-160.257 109.004,-145.227 109.004,-132.315\" fill=\"none\" stroke=\"black\"/>\n",
       "<polygon fill=\"black\" points=\"112.504,-132.095 109.004,-122.095 105.504,-132.095 112.504,-132.095\" stroke=\"black\"/>\n",
       "<text font-family=\"Times,serif\" font-size=\"14.00\" text-anchor=\"middle\" x=\"185.775\" y=\"-142.8\">TensorType(float32, scalar)</text>\n",
       "</g>\n",
       "</g>\n",
       "</svg>"
      ],
      "text/plain": [
       "<IPython.core.display.SVG at 0x105e31410>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "show_computation_graph(f_x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Same thing but x is a vector\n",
    "\n",
    "Using a vector for x lets us compute the sigmoid of a vector of values instead of doing it\n",
    "one-by-one"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x108b73090>]"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x10857ecd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = T.vector('x', dtype='float32')\n",
    "sigmoid_x = T.nnet.sigmoid(x)\n",
    "f_x = theano.function(inputs=[x], outputs=sigmoid_x)\n",
    "# without a for\n",
    "yvals = f_x(xvals)\n",
    "pl.plot(xvals, yvals)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/svg+xml": [
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   ],
   "source": [
    "show_computation_graph(f_x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Perceptron implementation\n",
    "\n",
    "We build a perceptron with a sigmoid activation function. That is\n",
    "\n",
    "$$o_i = sigmoid(W*x_i + b)$$\n",
    "\n",
    "Where $sigmoid(x) = \\frac{1}{1 + e^{-x}}$\n",
    "\n",
    "The error is simply ($y_i$ being the expected output value)\n",
    "\n",
    "$$e_i = (y_i - o_i)^2$$\n",
    "\n",
    "We train the network with minibatch SGD. That is, at each epoch, we compute the average gradient over a bunch of examples as opposed to a single one.\n",
    "\n",
    "$$W^{t+1} = W^t - \\eta \\frac{\\partial e_i}{\\partial W}$$\n",
    "$$b^{t+1} = b^t - \\eta \\frac{\\partial e_i}{\\partial b}$$\n",
    "\n",
    "Where $\\eta$ is the learning rate."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Error function derivative\n",
    "\n",
    "Note that if we add an entry set to 1 at the end of the x vector, we can transform our $Wx + b$ into $W\\hat{x} + b$ where $\\hat{x} = \\left[\\begin{matrix}x \\\\ 1 \\end{matrix}\\right]$\n",
    "\n",
    "$$l_i = W\\hat{x}$$\n",
    "\n",
    "$$o_i = sigmoid(l_i)$$\n",
    "\n",
    "$$e_i = (y_i - o_i)^2$$\n",
    "\n",
    "We want to compute the derivative of $e_i$ w.r.t $W$. From the [chain rule](http://en.wikipedia.org/wiki/Chain_rule), we have\n",
    "\n",
    "\n",
    "$$\\frac{\\partial e_i}{\\partial W} = \\frac{\\partial e_i}{\\partial o_i} \\frac{\\partial o_i}{\\partial l_i} \\frac{\\partial l_i}{\\partial W}$$\n",
    "\n",
    "With\n",
    "$$\\frac{\\partial e_i}{\\partial o_i} = -2(y_i - o_i)$$\n",
    "$$\\frac{\\partial o_i}{\\partial l_i} = sigmoid(l_i)(1 - sigmoid(l_i))$$\n",
    "$$\\frac{\\partial l_i}{\\partial W} = \\hat{x}$$\n",
    "\n",
    "Which gives us\n",
    "\n",
    "$$\\frac{\\partial e_i}{\\partial W} = -2(y_i - o_i) sigmoid(l_i)(1 - sigmoid(l_i)) \\hat{x}$$\n",
    "\n",
    "Which we use to update our weights at each step of gradient descent :\n",
    "\n",
    "$$W^{t+1} = W^t - \\frac{\\partial e_i}{\\partial W}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "# number of features\n",
    "X_dim = 2\n",
    "\n",
    "# weights\n",
    "W_init = 2 * (np.random.random(X_dim) - 0.5)\n",
    "W = theano.shared(\n",
    "    value=W_init.reshape(1, -1),\n",
    "    name='W',\n",
    "    borrow=True\n",
    ")\n",
    "\n",
    "# bias\n",
    "b_init = 2 * (np.random.random() - 0.5)\n",
    "b = theano.shared(\n",
    "    value = b_init,\n",
    "    name='b',\n",
    ")\n",
    "\n",
    "# data matrix\n",
    "X = T.matrix('X')\n",
    "# labels vector\n",
    "y = T.vector('y')\n",
    "\n",
    "y_pred = T.nnet.sigmoid(T.dot(W, X.T) + b)\n",
    "\n",
    "error = T.mean(T.sqr(y - y_pred))\n",
    "\n",
    "# compilation\n",
    "y_pred_fn = theano.function(\n",
    "    inputs=[X],\n",
    "    outputs=y_pred\n",
    ")\n",
    "\n",
    "error_fn = theano.function(\n",
    "    inputs=[X, y],\n",
    "    outputs=error\n",
    ")\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "# You can explore the computation graph as follow :\n",
    "if False:\n",
    "    show_computation_graph(error)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array(1.4242917014172882)"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# A forward pass through our perceptron\n",
    "error_fn(X=[[0, 1], [0, 2], [3, 4]], y=[0, 1, 2])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "# For backprop, we need the gradient with regard to our weights and bias\n",
    "g_W = T.grad(cost=error, wrt=W)\n",
    "g_b = T.grad(cost=error, wrt=b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.     ,  0.07662]])"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# We can compute the gradient wrt the weights as follow\n",
    "g_W_fn = theano.function(\n",
    "    inputs=[X, y],\n",
    "    outputs=g_W\n",
    ")\n",
    "\n",
    "# Gradient for X=[0, 1] and y=0\n",
    "g_W_fn(X=[[0, 1]], y=[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "# same for bias\n",
    "g_b_fn = theano.function(\n",
    "    inputs=[X, y],\n",
    "    outputs=g_b\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can check that theano's computed gradient match the derivation we made by hand.\n",
    "\n",
    "Note that this seems to run into numerical accuracy issues."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(array([ 0.     ,  0.10959]), array([ 0.10959]))\n",
      "[[ 0.       0.07662]] 0.0766240492623\n",
      "--\n",
      "(array([ 0.02558, -0.08954]), array([-0.12791]))\n",
      "[[ 0.01896 -0.06636]] -0.0948039833346\n"
     ]
    }
   ],
   "source": [
    "def sigmoid(x):\n",
    "    return 1 / (1 + np.exp(-x))\n",
    "\n",
    "def my_grad(X, y, W, b):\n",
    "    o = sigmoid(W.dot(X) + b)\n",
    "    # The last X is the derivative of o wrt X, which is X\n",
    "    gW = -2*(y - o)*sigmoid(o)*(1 - sigmoid(o))*X\n",
    "    # The last 1 is the derivative of o wrt b, which is 1\n",
    "    gb = -2*(y - o)*sigmoid(o)*(1 - sigmoid(o))*1\n",
    "    \n",
    "    return gW, gb\n",
    "\n",
    "X1 = np.array([0, 1], dtype=np.float32)\n",
    "y1 = np.array([0], dtype=np.float32)\n",
    "print my_grad(X1, y1, W.get_value(), b.get_value())\n",
    "print g_W_fn([X1], y1), g_b_fn([X1], y1)\n",
    "\n",
    "print '--'\n",
    "X1 = np.array([-0.2, 0.7], dtype=np.float32)\n",
    "y1 = np.array([0.5], dtype=np.float32)\n",
    "print my_grad(X1, y1, W.get_value(), b.get_value())\n",
    "print g_W_fn([X1], y1), g_b_fn([X1], y1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We could use g_W_fn to loop over our samples and update our weights. But theano has a nice *updates* parameters that you can give to the *theano.function*. It specifies which variables should be updated and how."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "learning_rate = 1\n",
    "updates = [\n",
    "    (W, W - learning_rate * g_W),\n",
    "    (b, b - learning_rate * g_b)\n",
    "]\n",
    "\n",
    "train_model = theano.function(\n",
    "    inputs=[X, y],\n",
    "    outputs=error,\n",
    "    updates=updates\n",
    ")\n",
    "\n",
    "predict = theano.function(\n",
    "    inputs=[X],\n",
    "    outputs=y_pred\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "prediction         [[ 0.62246]]\n",
      "---- iteration 0\n",
      "W, b before        [[ 0.5  0.5]] 0.0\n",
      "gradient wrt W, b  [[ 0.       0.29256]] 0.292560507054\n",
      "W, b after updates [[ 0.5      0.20744]] -0.292560507054\n",
      "prediction         [[ 0.47873]]\n",
      "---- iteration 1\n",
      "W, b before        [[ 0.5      0.20744]] -0.292560507054\n",
      "gradient wrt W, b  [[ 0.       0.23893]] 0.238933228816\n",
      "W, b after updates [[ 0.5     -0.03149]] -0.53149373587\n",
      "prediction         [[ 0.36286]]\n",
      "---- iteration 2\n",
      "W, b before        [[ 0.5     -0.03149]] -0.53149373587\n",
      "gradient wrt W, b  [[ 0.       0.16778]] 0.167778792514\n",
      "W, b after updates [[ 0.5     -0.19927]] -0.699272528385\n",
      "prediction         [[ 0.28935]]\n",
      "---- iteration 3\n",
      "W, b before        [[ 0.5     -0.19927]] -0.699272528385\n",
      "gradient wrt W, b  [[ 0.     0.119]] 0.118995825535\n",
      "W, b after updates [[ 0.5     -0.31827]] -0.818268353919\n",
      "prediction         [[ 0.24296]]\n",
      "---- iteration 4\n",
      "W, b before        [[ 0.5     -0.31827]] -0.818268353919\n",
      "gradient wrt W, b  [[ 0.       0.08937]] 0.0893734977481\n",
      "W, b after updates [[ 0.5     -0.40764]] -0.907641851668\n",
      "prediction         [[ 0.2116]]\n"
     ]
    }
   ],
   "source": [
    "W.set_value([[0.5, 0.5]])\n",
    "b.set_value(0)\n",
    "\n",
    "X1 = np.array([[0, 1]], dtype=np.float32)\n",
    "y1 = np.array([0], dtype=np.float32)\n",
    "print \"prediction        \", predict(X1)\n",
    "for i in xrange(5):\n",
    "    print '---- iteration', i\n",
    "    print \"W, b before       \", W.get_value(), b.get_value()\n",
    "    print \"gradient wrt W, b \", g_W_fn(X=X1, y=y1), g_b_fn(X=X1, y=y1)\n",
    "    train_model(X=X1, y=y1)\n",
    "    print \"W, b after updates\", W.get_value(), b.get_value()\n",
    "    print \"prediction        \", predict(X1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Important note\n",
    "\n",
    "Note that this is a naive implementation and it will suffer from one major problem if ran onto the GPU : the data (X) will be uploaded to the GPU on every call to our functions. This will most likely using the GPU will be slower than a CPU for this particular implementation.\n",
    "\n",
    "Of course, Theano allows you to avoid this and upload your data once to the GPU. The [logistic regression theano tutorial](http://deeplearning.net/tutorial/logreg.html) is a good reference for how to do minibatch training with the data in GPU memory. The key is to upload X and y once and then simply provide the index of the sample as an argument to our various functions."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Let's put everything in a class"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is a perceptron class that contains the same code as above, for ease-of-reuse"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "class Perceptron(object):\n",
    "    def __init__(self, X_dim, learning_rate=0.2):\n",
    "        # theano variable definitions\n",
    "        W_init = (2 * np.random.random(X_dim)) * 0.25\n",
    "        self.W = theano.shared(\n",
    "            value=W_init.reshape(1, -1),\n",
    "            name='W',\n",
    "            borrow=True\n",
    "        )\n",
    "        b_init = (2 * np.random.random()) * 0.25\n",
    "        self.b = theano.shared(\n",
    "            value = b_init,\n",
    "            name='b',\n",
    "        )\n",
    "\n",
    "        self.X = T.matrix('X')\n",
    "        self.y = T.vector('y')\n",
    "\n",
    "        self.y_pred = T.nnet.sigmoid(T.dot(self.W, self.X.T) + self.b)\n",
    "\n",
    "        self.error = T.mean(T.sqr(self.y - self.y_pred))\n",
    "        \n",
    "        self.g_W = T.grad(cost=self.error, wrt=self.W)\n",
    "        self.g_b = T.grad(cost=self.error, wrt=self.b)\n",
    "        \n",
    "        # theano functions\n",
    "        self.predict_fn = theano.function(\n",
    "            inputs=[self.X],\n",
    "            outputs=self.y_pred\n",
    "        )\n",
    "        \n",
    "        self.error_fn = theano.function(\n",
    "            inputs=[self.X, self.y],\n",
    "            outputs=self.error\n",
    "        )\n",
    "        \n",
    "        updates = [\n",
    "            (self.W, self.W - learning_rate * self.g_W),\n",
    "            (self.b, self.b - learning_rate * self.g_b)\n",
    "        ]\n",
    "\n",
    "        self.train_model_fn = theano.function(\n",
    "            inputs=[self.X, self.y],\n",
    "            outputs=self.error,\n",
    "            updates=updates\n",
    "        )\n",
    "        \n",
    "        # non-theano stuff\n",
    "        self.train_errors = []\n",
    "        self.validation_errors = []\n",
    "        \n",
    "    def train_gd(self, X_train, y_train, X_validation, y_validation, epochs=10):\n",
    "        \"\"\"Simple gradient descent training\"\"\"\n",
    "        assert len(X_train.shape) == 2, \"X must be 2D\"\n",
    "        \n",
    "        for epoch in range(epochs):\n",
    "            # This does forward propagation, gradient computation and weights\n",
    "            # update all in one\n",
    "            self.train_model_fn(X_train, y_train)\n",
    "            \n",
    "            # evaluate train/validation errors\n",
    "            self.train_errors.append(\n",
    "                self.error_fn(X_train, y_train)\n",
    "            )\n",
    "            self.validation_errors.append(\n",
    "                self.error_fn(X_validation, y_validation)\n",
    "            )\n",
    "        \n",
    "        return self\n",
    "                    \n",
    "    def predict(self, X):\n",
    "        \"\"\"Binary (0, 1) prediction\"\"\"\n",
    "        return self.predict_fn(X).astype(np.int)\n",
    "\n",
    "    def decision_function(self, X):\n",
    "        \"\"\"Float [0,1] prediction\"\"\"\n",
    "        return self.predict_fn(X)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Generate a toy dataset and test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[-0.11476 -0.14605]\n",
      " [ 1.26411  0.20133]\n",
      " [-0.19433  0.     ]\n",
      " ..., \n",
      " [ 1.36559  1.4677 ]\n",
      " [ 1.45857  1.13159]\n",
      " [ 2.13224  1.26225]]\n"
     ]
    }
   ],
   "source": [
    "def dataset_fixed_cov():\n",
    "    \"\"\"Generate 2 Gaussians samples with the same covariance matrix\"\"\"\n",
    "    n, dim = 300, 2\n",
    "    np.random.seed(42)\n",
    "    C = np.array([[0., -0.23], [0.83, .23]])\n",
    "    X = np.r_[np.dot(np.random.randn(n, dim), C),\n",
    "              np.dot(np.random.randn(n, dim), C) + np.array([1, 1])]\n",
    "    y = np.hstack((np.zeros(n), np.ones(n))).astype(np.int)\n",
    "    X = X.astype(np.float32)\n",
    "    y = y.astype(np.float32)\n",
    "    return X, y\n",
    "\n",
    "X, y = dataset_fixed_cov()\n",
    "\n",
    "print X"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x1093fbfd0>"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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JtrLZXbGJv5rBNamsY0wmMtus792lAO3rXoBQCgFvfJXXEYzXdc+mcrm6XGTt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\nQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x105e1b150>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pl.scatter(X[y==0, 0], X[y==0, 1], c='r')\n",
    "pl.scatter(X[y==1, 0], X[y==1, 1], c='b')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<__main__.Perceptron at 0x105e16b50>"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_train, X_validation, y_train, y_validation = skcross.train_test_split(X, y, test_size=0.33, random_state=20)\n",
    "perceptron = Perceptron(X.shape[1], learning_rate=0.2)\n",
    "perceptron.train_gd(X_train, y_train, X_validation, y_validation, epochs=800)\n",
    "#perceptron.train_minisgd(X_train, y_train, X_validation, y_validation, epochs=500, minibatch_size=10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x109884cd0>"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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+AHv2wF13wR//CDNmgOtLv+uOrWPcknEMbzOc1wa/RpUKVTwXqFKqTCiRN3xF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\npcohTf5KKVUO/T+sJZ7GlubchAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x105df4690>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pl.plot(perceptron.train_errors, label='train')\n",
    "pl.plot(perceptron.validation_errors, label='validation')\n",
    "pl.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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VAL6+95nx6ZgZUTKU3v4QRz9YCThCkSk6siC4lJWVUVZWFr3+4Q9/2HqdaVmm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\n9kYAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1099040d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from mpl_toolkits.axes_grid1 import make_axes_locatable\n",
    "import matplotlib.gridspec as gridspec\n",
    "\n",
    "def show_decision_boundary(clf, X, y, subplot_spec=None):\n",
    "    \"\"\"\n",
    "    Utility function to plot the decision function of a classifier\n",
    "    \"\"\"\n",
    "    assert X.shape[1] == 2\n",
    "    wratio = (15, 1)\n",
    "    if subplot_spec is None:\n",
    "        gs = gridspec.GridSpec(1,2, width_ratios=wratio)\n",
    "    else:\n",
    "        gs = gridspec.GridSpecFromSubplotSpec(1, 2, subplot_spec=subplot_spec, width_ratios=wratio)\n",
    "        \n",
    "    ax = pl.subplot(gs[0])\n",
    "    ax.set_title('Dataset and decision function')\n",
    "    \n",
    "    x_min, x_max = X[:,0].min() - 1, X[:,0].max() + 1\n",
    "    y_min, y_max = X[:,1].min() - 1, X[:,1].max() + 1\n",
    "    h = 0.2 # step size in the meshgrid\n",
    "    xx, yy = np.meshgrid(np.arange(x_min, x_max, h),\n",
    "                         np.arange(y_min, y_max, h))\n",
    "    xx = xx.astype(np.float32)\n",
    "    yy = yy.astype(np.float32)\n",
    "\n",
    "    Z = clf.decision_function(np.c_[xx.ravel(), yy.ravel()])\n",
    "    Z = Z.reshape(xx.shape)\n",
    "    ctr = ax.contourf(xx, yy, Z, cmap=cm.gray, vmin=0, vmax=1)\n",
    "    \n",
    "    unique_labels = np.unique(y)\n",
    "    colors = cm.Paired(np.linspace(0, 1, num=len(unique_labels)))\n",
    "    for i, yi in enumerate(unique_labels):\n",
    "        color = colors[i]\n",
    "        ax.scatter(X[y == yi, 0], X[y == yi, 1], c=color, linewidth=0, label='%d' % yi)\n",
    "    ax.legend()\n",
    "    ax.set_xlim((x_min, x_max))\n",
    "    ax.set_ylim((y_min, y_max))\n",
    "\n",
    "    pl.colorbar(ctr, cax=pl.subplot(gs[1]))\n",
    "\n",
    "show_decision_boundary(perceptron, X, y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Making a video of the training\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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YtmwZy5Yta5RzxZqoLsBfgEJV/WGYMZaobhgeLFE9sRGRdjjJ5lOBfcAnBCeq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\nK9JcrV2bmmS1bJm6/4gjUpOs++/P77xjBo5JSbL8WmdYt2E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      "text/plain": [
       "<matplotlib.figure.Figure at 0x10a865c50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.animation as manimation\n",
    "from tempfile import NamedTemporaryFile\n",
    "from matplotlib.legend_handler import HandlerLine2D\n",
    "\n",
    "# Depending on your environment, you might have to use any of the 2 following\n",
    "AVConvWriter = manimation.writers['ffmpeg'] # or 'avconv' if you're on ubuntu\n",
    "metadata = dict(title='Perceptron training', artist='',comment='')\n",
    "writer = AVConvWriter(fps=4, metadata=metadata, codec=\"libx264\", extra_args=['-vcodec', 'libx264'])\n",
    "\n",
    "#writer = manimation.FFMpegFileWriter(fps=4)\n",
    "\n",
    "perceptron = Perceptron(X.shape[1])\n",
    "\n",
    "fig = pl.figure(figsize=(10, 5))\n",
    "gs = gridspec.GridSpec(1, 2, wspace=0.4)\n",
    "\n",
    "nepochs = 800\n",
    "\n",
    "err_ymax = None\n",
    "\n",
    "with NamedTemporaryFile(suffix='.mp4') as f:\n",
    "    with writer.saving(fig, f.name, 100):\n",
    "        for epoch in xrange(nepochs):\n",
    "            perceptron.train_gd(X_train, y_train, X_validation, y_validation, epochs=1)\n",
    "            #perceptron.train_minisgd(X_train, y_train, X_validation, y_validation, epochs=1, minibatch_size=10)\n",
    "\n",
    "            if err_ymax is None:\n",
    "                err_ymax = max(np.max(perceptron.train_errors),\n",
    "                               np.max(perceptron.validation_errors)) * 1.1\n",
    "\n",
    "            if epoch % 10 == 0: # Capturing all 800 epochs takes forever...\n",
    "                show_decision_boundary(perceptron, X, y, gs[0])\n",
    "\n",
    "                ax = pl.subplot(gs[1])\n",
    "                pl.title('Error')\n",
    "                line_train, = ax.plot(np.array(perceptron.train_errors), c='b', label='train')\n",
    "                line_valid, = ax.plot(np.array(perceptron.validation_errors), c='g', label='validation')\n",
    "                ax.set_xlim(0, nepochs)\n",
    "                ax.set_ylim(0, err_ymax)\n",
    "                ax.set_xlabel('epochs')\n",
    "                ax.set_ylabel('error')\n",
    "                ax.legend((line_train, line_valid), ('train', 'validation'))\n",
    "\n",
    "                writer.grab_frame()\n",
    "            \n",
    "    video = open(f.name, \"rb\").read()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "bwAAAB1kYXRhAAAAAQAAAABMYXZmNTYuMTUuMTAy\n",
       "\" type=\"video/mp4\">\n",
       " Your browser does not support the video tag.\n",
       "</video>"
      ],
      "text/plain": []
     },
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from IPython.display import HTML\n",
    "\n",
    "VIDEO_TAG = \"\"\"<video style=\"width:80%\" controls>\n",
    " <source src=\"data:video/x-m4v;base64,{0}\" type=\"video/mp4\">\n",
    " Your browser does not support the video tag.\n",
    "</video>\"\"\"\n",
    "\n",
    "HTML(data=VIDEO_TAG.format(video.encode(\"base64\")))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Interesting links\n",
    "\n",
    "Tutorials :\n",
    "\n",
    "[Theano tutorials](http://deeplearning.net/software/theano/tutorial/)\n",
    "\n",
    "[Deep learning tutorials using Theano](http://deeplearning.net/tutorial/contents.html)\n",
    "\n",
    "Deep learning libraries using theano :\n",
    "\n",
    "[Lasagne](https://github.com/Lasagne/Lasagne)\n",
    "\n",
    "[Blocks](https://github.com/bartvm/blocks)\n",
    "\n",
    "[pylearn2](http://deeplearning.net/software/pylearn2/)\n",
    "\n",
    "General deep learning :\n",
    "\n",
    "[Reading recommendations](http://deeplearning.net/reading-list/)\n",
    "\n",
    "[Software](http://deeplearning.net/software_links/)\n",
    "\n",
    "[Stanford course about CNN](http://cs231n.stanford.edu/)\n",
    "\n",
    "Cool demos :\n",
    "\n",
    "[CNN in your browser](http://cs.stanford.edu/people/karpathy/convnetjs/)\n",
    "\n",
    "Misc :\n",
    "\n",
    "[How to access theano generated code](https://groups.google.com/forum/#!topic/theano-users/o-BLhLvnL5s)\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Additional stuff\n",
    "\n",
    "To add minibatch SGD training to the perceptron, use the following code. Note that since we do more weight updates per epoch (since we update for each minibatch), this requires less epoch to converge.\n",
    "\n",
    "    def train_minisgd(self, X_train, y_train, X_validation, y_validation, epochs=10, minibatch_size=10):\n",
    "        \"\"\"Training with minibatch SGD\"\"\"\n",
    "        assert len(X_train.shape) == 2, \"X must be 2D\"\n",
    "        \n",
    "        for epoch in range(epochs):\n",
    "            minibatch_indices = np.arange(X_train.shape[0])\n",
    "            np.random.shuffle(minibatch_indices)\n",
    "            # for each minibatch, compute gradient of weights\n",
    "            for start in xrange(0, len(minibatch_indices), minibatch_size):\n",
    "                end = start + minibatch_size\n",
    "                indices = minibatch_indices[start:end]\n",
    "                Xb = X_train[indices]\n",
    "                yb = y_train[indices]\n",
    "                \n",
    "                self.train_model_fn(Xb, yb)\n",
    "            \n",
    "            # evaluate train/validation errors\n",
    "            self.train_errors.append(\n",
    "                self.error_fn(X_train, y_train)\n",
    "            )\n",
    "            self.validation_errors.append(\n",
    "                self.error_fn(X_validation, y_validation)\n",
    "            )\n",
    "        \n",
    "        return self"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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